MinT - Information on Result #906907

Information on Result #906907

Linear OOA(49²⁴, large, F₄₉, 2, 5), using generalized (u,Â u+v)-construction based on

linear OOA(49⁰, 120100, F₄₉, 2, 0) (dual of [(120100, 2), 240200, 1]-NRT-code), using
- discarding factors / shortening the dual code based on linear OOA(49⁰, s, F₄₉, 2, 0) for arbitrarily large s, using
  - OOA with only one run / dual of NRT-code without redundancy [i]
linear OOA(49⁰, 120100, F₄₉, 2, 0) (dual of [(120100, 2), 240200, 1]-NRT-code) (see above)
linear OOA(49⁰, 120100, F₄₉, 2, 0) (dual of [(120100, 2), 240200, 1]-NRT-code) (see above)
linear OOA(49⁰, 120100, F₄₉, 2, 0) (dual of [(120100, 2), 240200, 1]-NRT-code) (see above)
linear OOA(49⁰, 120100, F₄₉, 2, 0) (dual of [(120100, 2), 240200, 1]-NRT-code) (see above)
linear OOA(49⁰, 120100, F₄₉, 2, 0) (dual of [(120100, 2), 240200, 1]-NRT-code) (see above)
linear OOA(49⁰, 120100, F₄₉, 2, 0) (dual of [(120100, 2), 240200, 1]-NRT-code) (see above)
linear OOA(49⁰, 120100, F₄₉, 2, 0) (dual of [(120100, 2), 240200, 1]-NRT-code) (see above)
linear OOA(49⁰, 120100, F₄₉, 2, 0) (dual of [(120100, 2), 240200, 1]-NRT-code) (see above)
linear OOA(49⁰, 120100, F₄₉, 2, 0) (dual of [(120100, 2), 240200, 1]-NRT-code) (see above)
linear OOA(49⁰, 120100, F₄₉, 2, 0) (dual of [(120100, 2), 240200, 1]-NRT-code) (see above)
linear OOA(49⁰, 120100, F₄₉, 2, 0) (dual of [(120100, 2), 240200, 1]-NRT-code) (see above)
linear OOA(49⁰, 120100, F₄₉, 2, 0) (dual of [(120100, 2), 240200, 1]-NRT-code) (see above)
linear OOA(49⁰, 120100, F₄₉, 2, 0) (dual of [(120100, 2), 240200, 1]-NRT-code) (see above)
linear OOA(49⁰, 120100, F₄₉, 2, 0) (dual of [(120100, 2), 240200, 1]-NRT-code) (see above)
linear OOA(49⁰, 120100, F₄₉, 2, 0) (dual of [(120100, 2), 240200, 1]-NRT-code) (see above)
linear OOA(49⁰, 120100, F₄₉, 2, 0) (dual of [(120100, 2), 240200, 1]-NRT-code) (see above)
linear OOA(49⁰, 120100, F₄₉, 2, 0) (dual of [(120100, 2), 240200, 1]-NRT-code) (see above)
linear OOA(49⁰, 120100, F₄₉, 2, 0) (dual of [(120100, 2), 240200, 1]-NRT-code) (see above)
linear OOA(49⁰, 120100, F₄₉, 2, 0) (dual of [(120100, 2), 240200, 1]-NRT-code) (see above)
linear OOA(49⁰, 120100, F₄₉, 2, 0) (dual of [(120100, 2), 240200, 1]-NRT-code) (see above)
linear OOA(49⁰, 120100, F₄₉, 2, 0) (dual of [(120100, 2), 240200, 1]-NRT-code) (see above)
linear OOA(49⁰, 120100, F₄₉, 2, 0) (dual of [(120100, 2), 240200, 1]-NRT-code) (see above)
linear OOA(49⁰, 120100, F₄₉, 2, 0) (dual of [(120100, 2), 240200, 1]-NRT-code) (see above)
linear OOA(49⁰, 120100, F₄₉, 2, 0) (dual of [(120100, 2), 240200, 1]-NRT-code) (see above)
linear OOA(49⁰, 120100, F₄₉, 2, 0) (dual of [(120100, 2), 240200, 1]-NRT-code) (see above)
linear OOA(49⁰, 120100, F₄₉, 2, 0) (dual of [(120100, 2), 240200, 1]-NRT-code) (see above)
linear OOA(49⁰, 120100, F₄₉, 2, 0) (dual of [(120100, 2), 240200, 1]-NRT-code) (see above)
linear OOA(49⁰, 120100, F₄₉, 2, 0) (dual of [(120100, 2), 240200, 1]-NRT-code) (see above)
linear OOA(49⁰, 120100, F₄₉, 2, 0) (dual of [(120100, 2), 240200, 1]-NRT-code) (see above)
linear OOA(49⁰, 120100, F₄₉, 2, 0) (dual of [(120100, 2), 240200, 1]-NRT-code) (see above)
linear OOA(49⁰, 120100, F₄₉, 2, 0) (dual of [(120100, 2), 240200, 1]-NRT-code) (see above)
linear OOA(49⁰, 120100, F₄₉, 2, 0) (dual of [(120100, 2), 240200, 1]-NRT-code) (see above)
linear OOA(49⁰, 120100, F₄₉, 2, 0) (dual of [(120100, 2), 240200, 1]-NRT-code) (see above)
linear OOA(49⁰, 120100, F₄₉, 2, 0) (dual of [(120100, 2), 240200, 1]-NRT-code) (see above)
linear OOA(49⁰, 120100, F₄₉, 2, 0) (dual of [(120100, 2), 240200, 1]-NRT-code) (see above)
linear OOA(49⁰, 120100, F₄₉, 2, 0) (dual of [(120100, 2), 240200, 1]-NRT-code) (see above)
linear OOA(49⁰, 120100, F₄₉, 2, 0) (dual of [(120100, 2), 240200, 1]-NRT-code) (see above)
linear OOA(49⁰, 120100, F₄₉, 2, 0) (dual of [(120100, 2), 240200, 1]-NRT-code) (see above)
linear OOA(49⁰, 120100, F₄₉, 2, 0) (dual of [(120100, 2), 240200, 1]-NRT-code) (see above)
linear OOA(49⁰, 120100, F₄₉, 2, 0) (dual of [(120100, 2), 240200, 1]-NRT-code) (see above)
linear OOA(49⁰, 120100, F₄₉, 2, 0) (dual of [(120100, 2), 240200, 1]-NRT-code) (see above)
linear OOA(49⁰, 120100, F₄₉, 2, 0) (dual of [(120100, 2), 240200, 1]-NRT-code) (see above)
linear OOA(49⁰, 120100, F₄₉, 2, 0) (dual of [(120100, 2), 240200, 1]-NRT-code) (see above)
linear OOA(49¹, 120100, F₄₉, 2, 1) (dual of [(120100, 2), 240199, 2]-NRT-code), using
- discarding factors / shortening the dual code based on linear OOA(49¹, s, F₄₉, 2, 1) for arbitrarily large s, using
  - appending 1 arbitrary column [i] based on linear OA(49¹, s, F₄₉, 1) (dual of [s, s−1, 2]-code) for arbitrarily large s, using
    - parity-check code [i]
linear OOA(49¹, 120100, F₄₉, 2, 1) (dual of [(120100, 2), 240199, 2]-NRT-code) (see above)
linear OOA(49¹, 120100, F₄₉, 2, 1) (dual of [(120100, 2), 240199, 2]-NRT-code) (see above)
linear OOA(49⁴, 120100, F₄₉, 2, 2) (dual of [(120100, 2), 240196, 3]-NRT-code), using
- appending kth column [i] based on linear OA(49⁴, 120100, F₄₉, 2) (dual of [120100, 120096, 3]-code), using
  - Hamming code H(4,49) [i]
linear OOA(49¹⁷, 2882402, F₄₉, 2, 5) (dual of [(2882402, 2), 5764787, 6]-NRT-code), using
- OOA 2-folding [i] based on linear OA(49¹⁷, 5764804, F₄₉, 5) (dual of [5764804, 5764787, 6]-code), using
  - discarding factors / shortening the dual code based on linear OA(49¹⁷, 5764805, F₄₉, 5) (dual of [5764805, 5764788, 6]-code), using
    - constructionÂ X applied to C_e(4) âŠ‚ C_e(3) [i] based on
      1. linear OA(49¹⁷, 5764801, F₄₉, 5) (dual of [5764801, 5764784, 6]-code), using an extension C_e(4) of the primitive narrow-sense BCH-code C(I) with length 5764800Â = 49⁴âˆ’1, defining interval IÂ =Â [1,4], and designed minimum distance dÂ â‰¥Â |I|+1Â =Â 5 [i]
      2. linear OA(49¹³, 5764801, F₄₉, 4) (dual of [5764801, 5764788, 5]-code), using an extension C_e(3) of the primitive narrow-sense BCH-code C(I) with length 5764800Â = 49⁴âˆ’1, defining interval IÂ =Â [1,3], and designed minimum distance dÂ â‰¥Â |I|+1Â =Â 4 [i]
      3. linear OA(49⁰, 4, F₄₉, 0) (dual of [4, 4, 1]-code), using
        discarding factors / shortening the dual code based on linear OA(49⁰, s, F₄₉, 0) (dual of [s, s, 1]-code) for arbitrarily large s, using
        OA with only one run / dual of code without redundancy [i]

Mode: Constructive and linear.

Optimality

Show details for fixed k and m, k and t, m and t.

Other Results with Identical Parameters

None.

Depending Results

The following results depend on this result:

	Result		This result only	Method
1	Linear OOA(49²⁴, large, F₄₉, 2, 4)	[i]		Strength Reduction for OOAs
2	Linear OOA(49²⁴, large, F₄₉, 2, 3)	[i]		Strength Reduction for OOAs